I'm not a lawyer; I'm not your lawyer 1
For the avoidance of doubt, the thrust of this debate is:
By placing a logo associated with a certain political movement near my user profile, does StackExchange violate Section 4(c) of the CC BY-SA 3.0?
Subscriber Content is Content that is contributed by StackExchange users. The relevant sections of CC BY-SA 3.0 (emphasis added) are:
c. ... The credit required by this Section 4(c) may be implemented in any reasonable manner; provided, however, that in the case of a Adaptation or Collection, at a minimum such credit will appear, if a credit for all contributing authors of the Adaptation or Collection appears, then as part of these credits and in a manner at least as prominent as the credits for the other contributing authors. For the avoidance of doubt, You may only use the credit required by this Section for the purpose of attribution in the manner set out above and, by exercising Your rights under this License, You may not implicitly or explicitly assert or imply any connection with, sponsorship or endorsement by the Original Author, Licensor and/or Attribution Parties, as appropriate, of You or Your use of the Work, without the separate, express prior written permission of the Original Author, Licensor and/or Attribution Parties.
d. Except as otherwise agreed in writing by the Licensor or as may be otherwise permitted by applicable law, if You Reproduce, Distribute or Publicly Perform the Work either by itself or as part of any Adaptations or Collections, You must not distort, mutilate, modify or take other derogatory action in relation to the Work which would be prejudicial to the Original Author's honor or reputation...
Does changing the logo on all pages imply an endorsement of the site/organisation by the user?
It is likely, though not definite, that this positioning of the logo will imply that the user endorses the website. However, actions taken by the user - such as creating an account, accepting the Terms, contributing content - are likely to affirm this view.
Does changing the logo imply that the site/organisation supports a particular political view?
Again, it is likely, not definite, that changing the logo will imply that the site/organisation supports a particular political view.
Does changing the logo impute support of a political view to the user?
In this case, however, it is highly unlikely that the change of logo would impute to the user support of the political view.
In a case such as this, onus of proof is on the plaintiff - were this claim brought in court, it would need to be proven on the balance of probability (or, less likely, on the preponderance of evidence) that a reasonable person would impute support of the marriage equality (and perhaps some other) agenda to the user. Reasonable person does not mean any particular person, nor does it mean, all people.
Part of the imputation must come from the purpose that the user subscribes to the site. Perhaps if StackOverflow were a site that promoted marriage equality or judicial activism, this could support an opinion that the user supports this view. However, StackOverflow is about programming, and programming doesn't imply that kind of agenda. Perhaps if the icon had been changed to something that suggested support for object-oriented programming, the icon could be taken to suggest that the user supports this agenda. Neither does the user's content suggest support for this cause - if they constantly made off-hand remarks about it in their posts, then perhaps, again, a reasonable person may make that imputation.
In any case, the damages awarded to the user would likely be compensatory rather than punitive - the user would need to therefore demonstrate actual suffering or loss as a result of the change of icon. If there were actual damages or loss, the way in which the user contributed to them - perhaps by posting a thread that would be likely to be inflammatory and attract attention to the user - may reduce an award of damages. In the case of no actual suffering or loss, the user could be awarded nominal damages.
Injunctions that could be awarded would need to be proportionate to the breach of license - the court could require references to this user to be anonymised. This is easily done. It is unlikely that the court would require all contribution by the user to be removed - this is unlikely to pass a public interest test.
In relation to placing a disclaimer in the footer, US courts have generally accepted disclaimers if they are positioned such that a reasonable user is likely to see it... In the footer? It's not a great place, and easily missed. It could be better than nothing, though, and may help with the likelihood of someone imputing such opinions to a user.
Essentially - it's extremely unlikely that a reasonable person would impute support of the marriage equality agenda on a user based on a logo change, because the support is not sufficiently connected to the primary purpose of the site, or the user's activities on the site.
Even if the user were successful in showing that this is the likely conclusion of a reasonable person, the remedies available to them would be limited to damages (which limited to actual losses, including suffering), and an injunction (which is likely to be anonymisation).
A disclaimer may not, on its own, actually preserve the validity of the license, but it may be useful on determining the likelihood of a reasonable person imputing opinions to a user.
1. This is larger than normal, because I think it is more important than normal.